\documentclass{ctexart}
\usepackage{avanti}
\everymath{\color{Solarized-magenta}}
\pagestyle{empty} % 没有页眉和页脚

 % define the plot style and the axis style
\tikzset{base/.style={smooth,thick,Solarized-base01}}
\tikzset{arrow/.style={->,>=stealth,base}}
\tikzset{curve/.style={base,Solarized-blue}}

\begin{document}

\begin{tikzpicture}

    \pgfmathtruncatemacro{\range}{1};

    \foreach \i in {-6,-3,0,3,6}
        {
            \draw [arrow] (\i,-1.3) -- (\i,1.3);
            \draw [arrow] (\i-1.3,0) -- (\i+1.3,0);
        }

    \pgfmathtruncatemacro{\o}{-6};
    \draw [curve,domain=0:90,variable=\t] plot({\o-cos(\t)^4},{sin(\t)^4});
    \draw [curve,domain=0:90,variable=\t] plot({\o-cos(\t)^4},{-sin(\t)^4});
    \draw [curve,domain=0:90,variable=\t] plot({\o+cos(\t)^4},{-sin(\t)^4});
    \draw [curve,domain=0:90,variable=\t] plot({\o+cos(\t)^4},{sin(\t)^4});
    \path (\o, -1.6) node () {$\ell_{0.5}$};

    \pgfmathtruncatemacro{\o}{-3};
    \draw [curve] (\o-\range,0) -- (\o,\range) -- (\o+\range,0) -- (\o,-\range) -- cycle;
    \path (\o, -1.6) node () {$\ell_1$};

    \pgfmathtruncatemacro{\o}{0};
    \draw [curve] (\o,0) circle (\range);
    \path (\o, -1.6) node () {$\ell_2$};

    \pgfmathtruncatemacro{\o}{3};
    \draw [curve,domain=0:90,variable=\t] plot({\o-cos(\t)^(1/2)},{sin(\t)^(1/2)});
    \draw [curve,domain=0:90,variable=\t] plot({\o-cos(\t)^(1/2)},{-sin(\t)^(1/2)});
    \draw [curve,domain=0:90,variable=\t] plot({\o+cos(\t)^(1/2)},{-sin(\t)^(1/2)});
    \draw [curve,domain=0:90,variable=\t] plot({\o+cos(\t)^(1/2)},{sin(\t)^(1/2)});
    \path (\o, -1.6) node () {$\ell_4$};

    \pgfmathtruncatemacro{\o}{6};
    \draw [curve] (\o-\range,-\range) rectangle ++(2*\range,2*\range);
    \path (\o, -1.6) node () {$\ell_\infty$};

\end{tikzpicture}


\end{document}